Is This Proof, or Not I was Fired for a Safety Violation, But Not Misconduct?

Is there any justification in being terminated for a safety violation ie." not wearing proper safety equipment" when it is the responsibility of the employer/ supervisor to physically sign out protective equipment from an enclosed and locked caged where only the supervisor has keys to issue employees PPE BEFORE hazardous job assignments are issued to the employee?

A Safety Violation is Enough to Justify Discharging an At Will Employee

You didn't mention which state this happened in, but the way you framed your question, suggests the possibility of an actual reason/argument you might use to rebut why the employer, at the time of discharge, failed to meet the burden of proving your actions amounted to work related misconduct.

Any prior written warnings about safety violation? Specifically, any for not wearing required PPE (personal protection equipment), before the final incident of not using a PPE caused your termination?

When assigned the task by your supervisor, did you ask for him/her to issue you the equipment so you could do your job? Did they refuse to unlock the cage, or room and get the PPE for you?

I for one .. think responsibility at work is often a shared concern, for both employees.

Meaning the supervisor (an employee) is aware of their responsibility to provide a subordinate with the PPE prior to performing any dangerous task requiring a PPE. And the subordinate employee should also be aware that without the PPE, they have a good reason to refuse to act on the directive from the supervisor .. until they they actually acquire the proper PPE for their own safety benefit.